In order to better understand the interaction between pore-fluidoverpressure and failure patterns in rocks we consider a porouselasto-plastic medium in which a laterally localized overpressure linesource is imposed at depth below the free surface. We solve numericallythe fluid filtration equation coupled to the gravitational force balanceand poro-elasto-plastic rheology equations. Systematic numericalsimulations, varying initial stress, intrinsic material properties andgeometry, show the existence of five distinct failure patterns caused byeither shear banding or tensile fracturing. The value of the criticalpore-fluid overpressure p(c) at the onset of failure is derived from ananalytical solution that is in excellent agreement with numericalsimulations. Finally, we construct a phasediagram that predicts thedomains of the different failure patterns and p(c) at the onset offailure.